Hendrik Jürges 119-2007

HEALTH INSURANCE STATUS AND PHYSICIANINDUCED DEMAND FOR MEDICAL SERVICES IN
GERMANY: NEW EVIDENCE FROM COMBINED
DISTRICT AND INDIVIDUAL LEVEL DATA
Hendrik Jürges
119-2007
Health insurance status and physician-induced
demand for medical services in Germany: new
evidence from combined district and individual level
data
Hendrik Jürges
Version 1.2: March 2007
MEA-Universität Mannheim
L13,17
68131 Mannheim
Germany
Email: juerges@mea.uni-mannheim.de
Fax: +49-621-181-1863
Abstract: Germany is one of the few OECD countries with a two-tier system of statutory and
primary private health insurance. Both types of insurance provide fee-for-service insurance,
but chargeable fees for identical services are more than twice as large for privately insured
patients than for statutorily insured patients. This price variation creates incentives to induce
demand primarily among the privately insured. Using German SOEP 2002 data, I analyze the
effects of insurance status and district (Kreis-) level physician density on the individual
number of doctor visits. The paper has four main findings. First, I find no evidence that
physician density is endogenous. Second, conditional on health, privately insured patients are
less likely to contact a physician but more frequently visit a doctor following a first contact.
Third, physician density has a significant positive effect on the decision to contact a physician
and on the frequency of doctor visits of patients insured in the statutory health care system,
whereas, fourth, physician density has no effect on privately insured patients' decisions to
contact a physician but an even stronger positive effect on the frequency of doctor visits than
the statutorily insured. These findings give indirect evidence for the hypothesis that
physicians induce demand among privately insured patients but not among statutorily insured.
Keywords: supplier-induced demand, health care utilization
JEL-Classification: I11
Acknowledgements: I am grateful to Martin Salm for helpful comments. I am also greatly
indebted to Dr. K.H. Wacker, Gummersbach, for raising my interest in this topic and
providing anecdotal evidence.
1
1. Introduction
This paper analyses the effects of individual health insurance status and local
physician density (the number of physicians per 100,000 inhabitants) on the individual
number of doctor visits in Germany, using data from the 2002 German Socio-economic Panel
(SOEP). The paper contains three innovations compared to earlier analyses based on earlier
waves of the same data set: first and foremost, I estimate separate count data models for
respondents insured in the German statutory health insurance system and privately insured
respondents. This is important because, although fees-for-service are generally fixed for
patients in either type of health insurance, they are more than twice as large for privately
insured patients. Physicians thus have a stronger incentive to induce demand among this
patient type. Second, I use district (Kreis-) level information on physician density (Germany
is divided into 439 districts). The information used in earlier studies was much coarser, and
thus less likely to capture the physician density that is relevant for the demand for doctor's
services.1 The third innovation is the use of an instrumental variable approach to account for
the potential simultaneity of physician density. In principle, the first stage of the IV-approach
models physician's location decisions and thus the (aggregate) supply of ambulatory health
care services.
Physicians have the opportunity to induce demand because – as in other markets for
credence goods such as car repairs or home maintenance – there are significant information
asymmetries in the medical market.2 Doctors are generally better informed about necessary
and appropriate diagnoses and treatments than their patients. After all, this is the very reason
why patients visit doctors, and exactly because doctors are better informed, it is their duty to
induce demand by informing patients about necessary and appropriate next steps in the
treatment of some disease. It is not the fair-minded attempt by the physician to convince a
patient of the necessity of some particular diagnostic test or treatment that health economists
have in mind when they talk of demand inducement. Rather, to talk of physician induced
demand, tests and treatments must not be medically indicated (including flat-of-the curve
medicine) and doctors must suggest them only for profit and not for medical reasons. The
question whether physicians systematically induce demand is contentious. Probably there is
no health care system without incentives for demand inducement, and many people may once
or twice have had the odd feeling that some diagnostic test or treatment was not strictly
1
For instance, Pohlmeier & Ulrich (1995) and Cassel & Wilke (2002) use physician density on the state level.
West Germany (until 1990) had 11 states. Post-unification Germany has 16 states.
2
See Dullek and Kerschbamer (2006) for a unifying review of the economic theory of credence goods.
2
necessary, but the important question is whether physician demand inducement is such a
widespread and significant phenomenon that it should instigate public intervention.
Physician density is probably the most commonly used variable in empirical studies of
physician-induced demand for health care services. Given the number and the average health
level of patients in a specific region, a higher physician density implies a shift of the
aggregate supply curve. Demand for medical services per physician decreases. When fees for
health care services are fixed, as this is the case in Germany, physicians cannot respond to
less demand by lowering their fees. Instead, they need to try to increase demand for their
services, both in terms of quality and quantity. A positive correlation between physician
density and health care utilization then indicates potential market problems. However, an
alternative explanation for a positive correlation between physician density and doctor visits
is that a higher physician density entails lower patients' opportunity costs of doctor visits, both
in terms of travel costs and shortened queues in the physician’s offices.
The empirical evidence on demand inducement is ambiguous. Early studies that find
positive effects of physician density on health care utilization in an instrumental variables
approach (simultaneity of physician density arises if one assumes that doctors tend to locate
where demand is high) are for example Fuchs (1978), Wilensky & Rossiter (1981), and
Cromwell & Mitchell (1986). In his classical article, Fuchs (1978) showed that a 10 percent
increase in the surgeon/population ratio results in a three percent increase in the number of
operations. Wilensky & Rossiter find an elasticity of 0.1 between physician density and the
frequency of follow-up visits to doctor's offices, and Cromwell & Mitchell find a surgery rate
elasticity with respect to surgeon concentration of 0.09. However, evidence against the
inducement hypothesis was also found e.g. by Sweeney (1982), McCarthy (1985), and Stano
(1985) for the US, or Carlsen & Grytten (1998) for Norway.
The early studies have been criticized because they provide at most indirect evidence
(Dranove & Wehner, 1994) or because the particular identification strategy was considered
inappropriate or flawed (e.g. Auster & Oaxaca 1981, Dranove & Wehner, 1994). A few recent
studies provide more direct evidence that corroborates the demand inducement hypothesis.
For instance, several studies show that physicians react to exogenous changes in
reimbursement rates (and hence exogenous changes in income) in a way that is consistent
with demand inducement: output (the number of visits) increases when reimbursement is
reduced, and vice versa (Rice 1983, Yip 1998). Gruber & Owings (1996) use the exogenous
decline in birth rates (in the 1970s and 80s) and hence exogenous decline in the income of
3
obstetricians and gynecologists to explain a substantial increase in the proportion of caesarean
deliveries. Moreover, they find a higher cesarean section rates for mothers with private health
insurance than for women covered by Medicaid or without coverage (also see Stafford 1990)
and even a larger increase in cesarean section rates in response to birth rate declines for
privately insured than for other mothers. These findings are noteworthy because relative
remuneration for cesarean delivery was much higher for the privately insured than for the
publicly insured or the uninsured.
Empirical studies of demand inducement in Germany using a variety of data sources
include Krämer (1981), Breyer (1984), Pohlmeier & Ulrich (1995), Cassel & Wilke (2002),
Thode et al. (2004), and Kopetsch (2007). Here the evidence is also mixed. Krämer (1981)
uses regional-level administrative data of statutory health insurances from the early 1970s and
finds that the number of doctors in region has a twice as large effect on aggregate health care
expenditures than the number of patients. This finding is consistent with demand inducement.
Breyer (1984) uses administrative data provided by the largest German statutory health
insurance (AOK) and estimates separate single-equation models for regions with a low and
high physician density. Although he finds a positive relationship between local physician
density and health care expenditures in both regressions, the gradient is steeper at low initial
levels of physician density than at high initial levels, which (in the light of a specific
theoretical model), is interpreted as evidence for an availability effect rather than an
inducement effect. Kopetsch (2007) uses detailed physician claims data and finds negative
effects of physician density on the average number of patients but positive effects on average
treatment intensity.
Pohlmeier & Ulrich, Cassel & Wilke, and Thode et al. combine survey data on
individual health care utilization with regional information on physician density. Pohlmeier &
Ulrich use 1985 SOEP data to estimate hurdle models, which separate the individuals' contact
from their frequency of contact decisions. They find no effect of physician density on the
probability of contacting a family doctor but significant positive effects on the number of
family doctor visits. Since the former probability can be viewed as purely demand driven but
the second combines demand and supply evidence, this finding is interpreted as evidence for
demand inducement and against the availability hypothesis. Cassel & Wilke use ECHP and
SOEP data for several years in the 1980s and 1990s and find no effects of physician density
on the probability and frequency of doctor visits. The same holds for Thode et al who use data
from the German health interview surveys.
4
The major drawback of the first set of studies is that they provide evidence only on
patients insured in the statutory health care system while those who are privately insured are
ignored due to data limitations. However, as is shown below, the distinction is vital because
of fundamentally different incentives in the two insurance systems. One shortcoming of the
latter set of studies is that physician density is measured on the state (Bundesland) level.
Estimates could be biased downwards because this information is too coarse to reflect the
relevant regional market for health care services. In particular for family doctors, the relevant
market is likely to be much smaller, probably on the town or in the case of larger cities even
on the neighborhood level. Non-findings can thus be explained by measurement error in the
main explanatory variable. Moreover, none of the above studies for Germany accounts
simultaneously for both alternative explanations for the positive physician density-health care
utilization: reverse causation and availability effects.
This paper is an attempt to remedy the above shortcomings by using data on physician
density on the district level, by explicitly modeling supply or doctors' location decisions, by
estimating negative binomial hurdle models and thus analytically separating contact and
frequency decisions, and by providing separate analyses for respondents with different
insurance status (statutory vs. private). The paper is organized as follows. Section 2 gives the
institutional background by briefly describing some salient features of the German health care
system. Section 3 describes the conceptual framework of this study. The data are described in
Section 4. After motivating the identification strategy chosen in this paper, Section 5 contains
the regression results. Section 6 gives a summary and conclusion.
2. Institutional background: insurance, fees, and incentives
About 90 percent of the German population are insured in the German statutory health
insurance system (SHI), see Colombo & Tapay (2004). SHI is financed by payroll taxes or
contributions. Contribution rates are independent of individual health risks and provide
coverage not only for the insured but also for non-employed dependents. In 2002, the SHI
system consisted of 350 different insurers or sickness funds, but services covered were (and
still are) highly regulated, so that there was no effective competition between them. SHI
provides free ambulatory care from family doctors and specialists – only in 2004 a copayment of €10 per quarter has been introduced.3 Physician's remuneration follows a fixed
3
During most of 2002, the Euro-US-Dollar exchange rate was about one-to-one.
5
fee-for-service schedule.4 For instance, in 2002, a short family doctor consultation (of less
than 10 minute length) earned about €5.60, and an ECG earned about €8.80. The €5.60 are
actually earned only for the 'first' consultation 'case', i.e. once per patient per quarter. Followup (short) consultations in the same quarter yield only about €1.35. Another noteworthy
feature of the SHI system is that doctors are paid directly by the insurers. Patients never learn
how much doctors actually charge for their services and have no idea about the (marginal)
costs of treatment. Willingness to pay is thus no barrier to "unproductive" treatments. Overall,
the SHI system as such provides no incentives to physicians and patients to restrict the
treatment to the medically necessary and to contain costs.
--- about here Figure 1 --Tenured civil servants, the self-employed, and employees who are above a certain
gross annual income threshold (€40,500 in 2002) are allowed to opt out of SHI and purchase
insurance in the private health insurance system (PHI), also see Figure 1.5 In 2002, about 50
insurance companies offered private health insurance. In contrast to the statutory health
insurers, private insurers offer a choice of contracts with different combinations of services
covered and deductibles. Physicians are paid directly by the patients who later get reimbursed
by their insurance. Patients who do not send in a claim during the course of a calendar year
usually get a rebate on their annual premium.
Opting out of the SHI system is attractive because private insurance premiums –
which are independent of income – are on average lower and more services are covered than
in the SHI.6 Premiums are lower because PHI has a much better risk pool than SHI. This is
not only due to the legal access constraints that effectively allow only better than average
health risks to join PHI. In contrast to SHI, private health insurers are allowed to differentiate
fees by age and sex (women pay more), to take individual risk premiums, and to reject bad
risks. Thus bad risks are systematically kept out of PHI risk pool. The opting out decision is
usually a one in a life-time decision (thus contracts are renewed year by year). Only
employees who become unemployed or whose income falls below the threshold are allowed
to return to the SHI system. The two main drawbacks of taking out private health insurance in
Germany are (1) insurance for non-employed dependants is not free and (2) insurance
4
Each service is awarded a specific number of points that reflects the relative value of this service. The value of
one point varies across regions and over time. In 2002, one point earned approximately 4 Cent.
5
About 10 percent of the population are privately insured. Less than 0.5 percent of the population have no health
insurance.
6
This holds especially for tenured civil servants. Another particularity of the German health care system is that
the state covers half of the civil servants' health care costs, so that civil servants only need to buy private health
insurance with 50% coverage.
6
premiums can rise considerably over time and with age, depending on the development of the
particular risk pool of an insurer.7
Insurance status (statutory vs. private) potentially affects the demand for and supply of
health care services in Germany. Patients with a private health insurance are attractive from
the doctors' viewpoint because they can be charged much higher (but still legally fixed) fees
for the same services as SHI patients. Remuneration for services to privately insured patients
follows a similar fee-for-service schedule as remuneration for services to the statutorily
insured. In 2002, the 'basic fee' was €5.66 for a short family doctor consultation and €8.86 for
an ECG (thus pretty much the same as for the same services rendered to SHI insured patients).
However, physicians are allowed to charge up to 2.3 times the basic fee if a case is more
difficult than usual and up to 3.5 times the basic fee in special cases. In practice of course,
physicians always charge at least 2.3 times the basic fee.8 A short family doctor consultation
of a privately insured patient thus earns about €13 and an ECG earns €20.78 (compared to
€5.60 and €8.80 for a statutorily insured patient). Similar relationships hold for all other
services. Utility maximizing physicians thus face a kinked budget constraint which would
make it rational to first serve all privately insured patients if that was feasible. In fact,
privately insured patients get preferential treatment at some doctors' offices, for instance by
getting appointments much quicker than others, buy jumping queues at the doctors offices, or
by more comfortable waiting rooms. Older physicians also often choose some kind of semiretirement by treating only private patients. Moreover, if physicians induce patients to
demand services beyond the medically indicated level, they behave rationally if they do so
primarily for the privately insured (if necessary at the expense of patients in the statutory
health insurance).
3. Conceptual framework
In this section, I will briefly outline the conceptual framework that motivates the
empirical analysis. Individual health care utilization is assumed to be determined by supply
and demand factors in a multi-stage process (cf. Manning et al. 1981). Here, we consider a
four-stage model. In the first stage, doctors choose locations for their practices. In the second
stage, patients contact doctors. In the third stage doctors recommend treatments and in the
7
A full analysis of individual insurance choice is beyond the scope of this paper. To my knowledge, there is only
one microeconometric study so far (Rohweder 1995).
7
fourth stage, patients decide whether to comply with the recommendation. I will describe each
stage in turn and discuss the role of physician density and patients' insurance status.
Doctors choose the location that maximizes their expected utility, which is a function
of income, leisure, 'psychic' inducement costs, and location-specific amenities (location
decision). Income depends positively on the number of patients – which in turn is a function
of physician density and the average health level of the local population – and on the
proportion of privately insured patients. Leisure depends negatively on the number of patients
but not on the proportion of privately insured patients. Everything else equal, physicians
prefer regions with a large proportion of ill persons and regions with a large proportion of
privately insured patients.
In the second stage, patients who feel ill decide whether to contact a physician in their
region (contact decision). Whether a patient feels ill within a specific period can be viewed as
the outcome of a random process that is influenced by a patient's health status. Whether a
doctor is contacted when a patient feels ill depends, among other things, on the local
physician density. A higher physician density reduces the patient's cost and thus increases the
probability of a patient-doctor contact. But ceteris paribus, a higher physician density
decreases the number of contacts per physician, so that the net effect of higher physician
density on the number of initiated contacts per physician is unclear. Whether patients contact
a doctor should also depends on insurance status. As mentioned in the preceding section,
privately insured patients may have lower opportunity costs of visiting a doctor because they
get preferential treatment. On the other hand, the privately insured are discouraged from
visiting a doctor for minor ailments because of deductibles and rebates.
In the third stage, the physician informs the patients about their health status and
suggests some treatment (intensity). The medically indicated treatment intensity is determined
solely by the patients' true (latent) health status. Note that neither the number of patients who
initiate contact, nor the private-statutory mix of those who initiate contact, nor the indicated
treatment intensity can be influenced by the physician once the practice location is chosen. It
is at this stage when the physician has the opportunity to induce demand. Consider the
following simple model (largely borrowed from Gruber & Owings (1996)):
Since the physician's location is already fixed at this stage, we neglect location specific
capital. Let physician utility be given by the additive separable function U = u(Y) - v(I) with
8
The fact that PHI insurance premiums are on average lower than SHI contributions although treatments of the
privately insured cost more than twice as much reflects how unequal risks are distributed between the two
systems.
8
u' > 0, u'' < 0, v' > 0 and v'' > 0, and where Y denotes full income (earnings minus the value of
forgone leisure) and I is total inducement,. Function v reflects the physician's disutility from
inducement. Income equals fees-for-service times the number of services provided:
Y = YPP + YSS, where P and S denote services to privately and statutorily insured patients,
respectively. YP and YS are the respective (exogenous) fees with YP > YS. In the following,
we normalize YS to one, hence YP > 1. P and S are determined by the number of contacts C,
the proportion of privately insured patients π, and the amount of inducement per patient i:
P = π C f(iP) and S = (1 - π) C f(iS). The inducement function f is increasing and concave with
f(0) = 1. If the function was linear, it would be optimal to sell services only to privately
insured patients. Total inducement equals the aggregate amount of inducement per patient:
I = π C iP + (1-π) C iS. Finally, iP and iS are assumed to be non-negative. This assumption
essentially means that doctors never reject or willingly undertreat patients that have contacted
them.9
The physician chooses iP and iS to maximize U. The first order conditions are:
∂U / ∂iP = u' YP π C f'(iP) – v' π C ≤ 0; iP ≥ 0; iP ∂U / ∂iP = 0
and
∂U / ∂iS = u' (1-π) C f'(iS) – v' (1-π) C ≤ 0; iS ≥ 0; iP ∂U / ∂iS = 0
Let us consider only the interior solution with iP > 0 and iS > 0. Then the following
optimality condition can be derived (where stars indicate optimal values):
YP f'(iP*) = f'(iS*)
This condition states that the marginal income from inducing a privately insured
patient must equal the marginal income from inducing a statutorily insured patient. YP is
greater than 1, hence iP* > iS*. Since fees for services to privately insured patients are higher
than fees for services to statutorily insured, biased suggestions should be primarily given to
the former type of patient. Comparative static analysis of the model shows that inducement
per patient (private and statutory) decreases when C increases, i.e. when physician density
falls. If physician density falls sufficiently or the relative fee for services to private patients
YP is sufficiently high, physicians might also find themselves at corner solutions with iP > 0
and iS = 0 or with no inducement at all.
9
Relaxing this assumption would provide an interesting extension of the model because it allows optimal
solutions where doctors induce private patients' demand and simultaneously reject statutorily insured patients (or
put them on long waiting lists). However, one would presumably also have to change the assumptions about the
utility function, because deliberately not treating a patient will also cause disutility.
9
In the fourth stage, patients decide about their compliance with the doctor's
recommendation (also known as the frequency decision). The degree of compliance depends
on the expected benefits and costs (direct and indirect) of treatment. Benefits are inversely
related to patient's self-perceived health status. With regard to costs, similar arguments apply
as in the contact decision stage: physician density reduces indirect costs by reducing travel
and waiting times and privately insured patients have lower opportunity costs because of
preferential treatment.
The empirical model estimated in this paper will not distinguish between the third and
fourth stage of the process. With household survey data one usually observes only the joint
outcome, i.e. the realized number of visits. The estimated model will consist of three
equations, one for the first stage, explaining aggregate location choice, one for the second
stage, explaining the probability of contact, and one joint equation for the third and fourth
stages taken together (frequency decision).
4. Data description
The data used in this study combine survey data on individual health care utilization
drawn from the 2002 wave of the German Socio-Economic Panel (SOEP) with indicators on
the regional level, specifically on the Kreis (district) level, which were mainly drawn from the
2004 regional database (INKAR) of the Federal Office for Building and Regional Planning
(BBR). In the following, I describe each data in turn.
4.1. Individual level data
SOEP respondents are asked to report the number of doctor visits during the last three
months. The 2002 wave does not discriminate between family doctor and specialist visits. 31
percent of all SHI patients and 37 percent of PHI patients have not seen a doctor at all during
these three months (see Figure 2). Nearly 80 percent of the sample visited a doctor three times
or less. Only 3.5 percent of the sample reported more than 10 visits. The average number of
physician visits in the SHI and PHI samples is 2.57 and 2.31, respectively, with standard
deviations variances equal to 4.24 and 3.99, indicating substantial overdispersion. Conditional
on visiting a doctor at least once, the average number of doctor visits was about 3.7 in both
subsamples (only marginally larger for SHI patients). The number of visits is highly skewed.
--- about here Figure 2 ---
10
The explanatory variables in the working sample are described in Table 1, separately
for SHI and PHI respondents. The full sample has 22,417 observations, of which 3,245 (14.5
percent) are privately insured. 40 percent of the privately insured have a deductible.10 As
mentioned above, the proportion of privately insured individuals in the population is about 10
percent. Thus the privately insured are overrepresented in our data. One of the reasons to use
the 2002 SOEP wave is that in this year, a supplement of high income households has been
added to the SOEP. 44.2 percent of the individuals in this supplement were privately insured
(compared 10.7 percent in the original sample), thus increasing the statistical power when
separate regressions are run for SHI and PHI respondents.
--- about here Table 1 --The SHI and PHI subsamples differ in a number of important respects. In particular,
privately insured respondent are in better self-rated health. 49 percent of the SHI sample,
compared to 60 percent of the PHI sample, say they are in good or very good health, and 12
percent versus 10 percent have been in a hospital in the preceding year. Note that the health
difference can be found despite the fact that the privately insured are on average nearly one
year older. Still, as explained above, it is not surprising to find the privately insured sample in
better health. In addition to the fact that they have most likely passed a health screening
before taking out private health insurance, they are predominantly male, have nearly three
years more formal education and much higher income. The median equivalent income in the
SHI sample was 17,747€ compared to 30,282€ in the PHI sample.11 Among the privately
insured, more people work full-time, and less people work part-time or do not work.
Considering how selection into private health insurance works (see the minimum income
threshold), this is not surprising either.
It should be noted that despite the fact that privately insured respondents are much
healthier and wealthier, they visit doctors only slightly less often than respondents insured in
the statutory health insurance. In fact the difference in the number of doctors visits is not
statistically significant. Thus conditional on health, it appears as if physicians treat the
privately insured more intensely. This issue will be analyzed in greater detail in Section 4.
10
Privately insured respondents without deductible are found predominantly among civil servants. In their case,
the employer pays at least 50 percent of the sickness costs, and only the rest needs to be covered by a private
insurance. To the best of my knowledge, private insurers do not offer contracts with deductibles to civil cervants.
Interestingly, the employer's part of the insurance has a deductible, but it does come by a completely different
name (Kostendämpfungspauschale), so that many civil servants may actually not be aware of the fact that they
have a deductible indeed.
11
Individuals living in households with implausibly low income (<3600 Euro per year; 111 households) have
been excluded from the sample.
11
4.2. District level data
The bottom of Table 1 contains information on the district level. Of the 439 districts in
Germany, the SOEP data covers 434. The INKAR 2004 database is a rich source of statistical
information on the district level in Germany (for the year 2002). Physician density, measured
as the number of physicians per 100,000 inhabitants, is the most interesting variable in the
context of this study.12 It ranges from 70 (Saalkreis) to 383 (Heidelberg) with a mean of 150
and a standard deviation of 51. We have thus sufficient regional variation in this variable for
an informative empirical analysis.
As mentioned before, I use an instrumental variable approach to account for the
potential simultaneity of physician density. Suitable instruments are variables that affect the
location decision of physicians but have no direct effect on the number of doctor visits of
individuals observed in the SOEP. The instruments used here are log income per capita in the
district, the percentage of inhabitants aged 65 and over living in the district and whether the
district has a medical school.
Data on the first two instruments are drawn from the INKAR database. Gross income
per capita serves as a proxy for a whole host of amenities that make a particular region
attractive in individual location decisions. Per capita gross income ranges from 11,300€
(Südwestpfalz, Zwickauer Land) to 80,600€ (München). Doctor density is expected to be
higher in high income regions, for instance because high income regions might provide better
employment opportunities for physicians' spouses, or better schools for physicians' children.
The number of privately insured patients might also be higher, which offers better earning
opportunities for physicians.
Since older individuals are on average less healthy and need doctors services more
often, this variable indicates the aggregate demand for medical services in the population. It is
assumed that doctors tend to locate where demand his relatively high. The average percentage
of inhabitants aged 65 and over is 17.7. It has standard deviation 1.9 and it ranges from 12.4
(Freising) to 23 (Pirmasens). One argument that could be brought forward against this
instrument is that the direction of causality might also go in the opposite direction: less
healthy people tend to locate in regions where there is a large supply of medical services.
12
The number of physicians includes those providing ambulatory services under contract of the regional doctors'
association (Kassenärztliche Vereinigung). Such a contract is a necessary condition to treat patients insured in
the German statutory health care system. Physicians who exclusively treat privately insured patients (less than
5% of all physicians providing ambulatory services) are thus not included here.
12
However, given the low geographical mobility of older people, it seems unlikely that this is an
important causal pathway.
The third instrument is a dummy variable that captures whether a medical school is
located in the district. There are 43 such districts in Germany. The argument behind this
instrument is that people are to some extent regionally immobile. Physicians in Germany who
start practicing on their own are typically between 35 and 40 years old (cf. Kassenärztliche
Bundesvereinigung 2003, Table I.21). Starting physicians will thus often have lived for a
substantial number of years in or close to a city where a medical school is located and have
built up location-specific capital, so that regional mobility tends to be low.
5. Model estimation and results
In order to separately estimate the contact and frequency decision stages, I follow
Pohlmeier & Ulrich (1995) and Gerdtham (1997) in computing negative binomial hurdle
model. Hurdle models treat the decision to contact a physician at all and the decision how
often to visit the physician can be treated as different stochastic processes. They consist of
two parts, which can be estimated by separate maximizations of the likelihood functions
(Mullahy 1986). In the first part of the model, our key variable physician density reflects the
regional availability of doctors to patients. The second part of the model analyses the
individual number of doctor visits only for those who visited a doctor at least once in the
reference period. Only in this second part, a positive coefficient of physician density on the
number of doctor visits is interpreted as evidence for physician induced demand. One
advantage of hurdle model is that it allows the same variables to have effects of different
signs on the contact decision and the frequency decision.13
Formally, the hurdle model is specified as follows (cf. Deb & Trivedi 2006). Let the
probability of positive counts (conditional on covariates X) be determined by some density
function
f1 : Pr[ y > 0] = 1 − Pr[ y = 0] = 1 − f1 (0) . The number of (positive) counts is
determined by a truncated density function f 2 ( y | y > 0) = f 2 ( y ) /(1 − f 2 (0)) , which is
multiplied by Pr[ y > 0] = 1 − f1 (0) to ensure that probabilities sum to one. The stochastic
process of the hurdle model can then be written as
13
This assumption can be tested statistically by comparing the log likelihood of the hurdle model (which is the
sum of the two parts' log-likelihoods) with the log likelihood of a (single equation) negative binomial model.
With the data used in this paper, the single equation model is clearly rejected.
13
f1 (0)
if y = 0
⎧
g ( y) = ⎨
⎩[1 − f1 (0)] f 2 ( y | y > 0) if y > 0
with log-likelihood function
⎛
⎞
log L = ∑ g ( y ) = ⎜ ∑ ln f1 (0) + ∑ ln[1 − f1 (0)] ⎟ + ∑ ln f 2 ( y | y > 0) .
⎜ y =0
⎟ y >0
y ≥0
y >0
⎝
⎠
This shows that the log-likelihood function can be written as the sum of a binomial
probability part (in parentheses) and a truncated count model part.
The meaningful distinction between contact and frequency of contact decision in a
hurdle model entails two assumptions. First, there must not be more than one sickness spell
within the reference period. Second, the first count in the reference period actually constitutes
a first contact related to a sickness spell and not a follow-up visit belonging to sickness spell
that started before the reference period. Of course, either assumption will almost certainly be
violated in a few cases. How many cases are concerned obviously depends on the length of
the reference period. The longer the reference period, the larger the number of multiple
sickness spells but the smaller the probability that the first registered contact belongs to
sickness spell from a preceding period, and vice versa. The optimal length of the reference
period is a priori unclear, but the three months used in the SOEP appear to be fairly good
compromise (cf. Pohlmeier & Ulrich 1995, Gerdtham 1997).
5.1. Instrumenting physician density
To account for the potential simultaneity of physician density, I follow a two-step IVtype procedure (cf. Mullahy 1997, Winkelmann 2000). In the first step I predict physician
density by OLS, using the three instruments described above: the average gross income in the
district, the proportion of people older than 65 living in the district, and a dummy variable that
indicates whether the district has a medical school. The predicted values are then used in the
second step two-part model instead of the original value of physician density. Standard errors
that account for the inclusion of estimated variables in the second step are computed by
bootstrapping (repeating the full estimation procedure including first and second estimation
steps 200 times).
Instrumental variables are always subject to close scrutiny. First, the instruments must
not be weak, i.e. they must be sufficiently correlated with the endogenous regressor. A
recently established rule-of-thumb criterion for good instruments is an F-statistic larger than
14
10 in a test of joint significance in the first stage regressions (cf. Staiger & Stock, 1997, but
note that the rule-of-thumb was developed for the linear 2SLS model). On that account, my
instruments perform quite well. Table 2 shows the parameter estimates and test results for the
first step regressions, i.e. for the full sample and for the separate samples. Note that standard
errors are cluster adjusted, i.e. they are computed as if the full sample regression contained
only 434 observations (of districts). The F-statistics are larger than 55 and thus well above the
threshold of 10 in all three models. Including the instruments in the first step raises the Rsquared by more than 60 percentage points, i.e. the instruments have substantial explanatory
power.
--- about here Table 2 --In terms of their signs, the instrumental variables have the expected effects on
physician density. Districts with higher per capita income, districts with a large proportion of
older inhabitants, and districts with a medical school have a higher physician density than
others. Only few of the individual level variables are significantly related with doctor density.
Districts with a higher physician density are characterized by a lower proportion of married
individuals, and a higher proportion of better educated, two variables that possibly reflect the
degree or urbanization.
Another concern about instrumental variables is that the identifying (exclusion)
restrictions may not hold. In the context of this paper, the exclusion restrictions hold if
average district income, the percentage of individuals aged 65 and over living in a district, and
the presence of a medical school do not directly affect the likelihood and frequency of doctor
visits of an individual living in the district. If there is an effect, it must be only indirect, i.e.
through the correlation of the instruments with physician density. This assumption sounds
plausible, and although exclusion restrictions cannot be tested formally, one can at least check
whether the instruments have an independent effect on the outcome variables by including
them in the outcome regression along with the variable that is to be instrumented. The Chisquared statistics for the joint significance of the instruments in the two outcome equations
are 3.40 and 3.53 (with 3 degrees of freedom), respectively, in the full sample, 3.17 and 3.04
in the SHI subsample, and 3.13 and 0.26 in the PHI subsample (detailed regression results not
shown). The corresponding P-values are .33 and .32, .37 and.36, and .38 and .97. In other
words, the instruments appear to have no independent effect on the probability of visiting a
doctor and the number of doctor visits.
15
5.2. The probability of physician visits
The first part of the hurdle model used to analyze the probability of contact is a
logistic regression model.14 Results without and with correction for possible simultaneity of
physician density are shown in Table 3. Let us begin with a discussion of the full sample
results (column 1 and 2). A positive effect of physician density on the probability of contact is
found regardless of whether physician density is instrumented. Assuming that the first contact
is solely demand driven, the positive effect of physician density can be interpreted as the
effects of reduced opportunity costs or increased availability. Without taking into account
potential simultaneity, the logit coefficient of log physician density is about .15 and
significant at the 1 percent level. The coefficient can be roughly interpreted as an elasticity,
i.e. when physician density rises by 1 percent, the probability that a physician is contacted
(conditional on heath and other covariates) rises by 0.15 percent. When simultaneity is taken
into account, the effect size is only slightly smaller, but standard errors increase so much that
the effect is no longer statistically significant even at the 5 percent level. However, the
difference between both estimates is statistically insignificant, so that one cannot reject the
null hypothesis that physician density is in fact exogenous. This holds not only for the logit
model in the full sample but for all estimation parts in all samples. For this reason, I will
restrict the following discussion to the standard regression results (but all IV-estimates are
still shown for interested readers).
--- about here Table 3 --Privately insured respondents are less likely to have seen a doctor at all in the
preceding three months. Note that this is conditional on observed health.15 Plausible
explanations for this finding have been mentioned before. First, insurance status might reflect
unobserved health status since private insurance companies are allowed to screen applicants
and to reject bad risks. Second, in contrast to patients covered by the statutory health system,
privately insured patients first pay the doctors bill and get reimbursed later (even if they have
full coverage), i.e. they do not have the illusion of zero marginal costs. Deductibles and
rebates should further discourage doctor visits for minor ailments. In fact, for patients with
deductibles, the estimated probability of visiting a doctor is further reduced, but the difference
to privately insured without deductible is statistically insignificant.
14
This corresponds to the specication chosen by Gerdtham (1997). Pohlmeier & Ulrich (1995) use a negative
binomial model in the contact decision part of their estimations.
15
Including more detailed health information (SOEP 2002 contains a variant of the SF12 questionnaire) does not
change this result.
16
When the sample is split into statutorily and privately insured individuals (see columns
3 to 6), an interesting picture emerges. Whereas the effect of physician density is still positive
and significant in the SHI sample (with an elasticity of about 18 percent), it vanishes for
privately insured patients. This means that demand for health care services of statutorily
insured respondents is affected by changes in opportunity costs related to physician density
but that the demand of the privately insured is not. This result is plausible because the
privately insured can jump queues formed by the statutorily insured patients at some doctors'
offices, an issue that often gives rise to health care equity debates in the German public.
Again, the effect of deductibles on contact is negative but insignificant.
Let us also briefly discuss the effects of the other covariates. First note that with one
exception (part-time employment), the estimated coefficients are very similar across samples
and estimation methods. Moreover, they are mostly according to expectations and in line with
earlier studies for Germany (e.g. Pohlmeier & Ulrich, 1995). Expectedly, the largest effects
on the decision to contact a physician can be found for self-rated general health and for
hospital stays in the preceding year (as a more objective health indicator). The odds of visiting
a doctor at least once are about 4.5 times larger for respondents in very poor self-rated health
than for those in fair health (the reference category). Likewise, those in very good health have
odds that are about one third as large as those of the reference category.16 Hospital stays in the
preceding year lead to about 2.5 higher odds of physician contacts.
Conditional on all covariates, the probability of having visited a doctor in the last three
months first decreases in age and then increases in age. The minimum is reached at about age
40. Women are substantially more likely to visit doctors even if self-rated health status is
controlled for, and married individuals are more likely to contact doctors than others. This
holds particularly for men, as the large interaction effect of marital status with sex reveals.
Better educated and higher income individuals also show a higher likelihood of visiting a
doctor. Since this effect is measured conditional on health, it might reflect the tendency of
better educated and higher income individuals to care more for their health (higher allocative
efficiency or stronger preferences for the future, cf. Grossman 2005). It might also reflect
socio-economic inequality in access to health care (e.g. Gerdtham 1997). Full-time employed
respondents are significantly less likely to contact a physician. which is probably largely a
matter of opportunity costs. Part-time employees in the statutory health care system are also
less likely to contact a physician than the reference group, whereas privately insured part-time
16
Odds ratios are obtained by exponentiating the logit coefficients. In contrast to marginal effects obtained from
probit regressions they are constant across different values of the other explanatory variables.
17
employees are more likely, but the difference to respondents who are not working is not
significant.
5.3. The frequency of doctor visits
The frequency of doctor visits is analyzed conditional on visiting a physician at least
once in the last three months using the zero-truncated negative binomial model. Results for
the different samples without and with correction for possible simultaneity of physician
density are shown in Table 4.
Physician density has a significant positive relationship with the number of doctor
visits. This holds in the full sample and in the two subsamples, independent of whether
potential simultaneity is dealt with. Instrumenting physician density actually increases the
point estimates, but as was mentioned above, the Hausman-test never rejects the null
hypothesis of exogenous physician density. Since physician density enters the regression
equation in logarithms, its coefficient can be interpreted as an elasticity. Thus a one percent
increase in physician density raises the number of doctor visits among all respondents by 0.17
percent. Overall, the effect size is in the range of findings found in the US (e.g. Stano 1985,
Cromwell & Mitchell 1986).
Note that insurance status has a fundamentally different effect on the frequency of
doctor visits than on the contact decision. While the privately insured are less likely to contact
a doctor, their number of doctor visits is significantly larger than that of patients covered by
statutory health insurance. If the privately insured are on average healthier, one can expect
them also to visit their doctor less often. One possible explanation for this seemingly
contradictory finding is that physicians treat privately insured patients differently. Just
because the health services rendered to a privately insured individual pay so much better than
the same services rendered to individuals insured in the statutory health insurance, physicians
have an incentive to sell unnecessary diagnoses and ineffective treatments to the privately
insured. Separating the sample by insurance status corroborates this interpretation. It reveals
that the estimated effect among privately insured is about 1.6 times as large as among
statutorily insured (with an. the elasticity of 27 versus 16 percent). The difference is not
statistically significant, however, due to the large standard errors estimated for the privately
insured.
--- about here Table 4 ---
18
The frequency of physician visits given contact is assumed to be determined by
demand as well as supply factors. Viewed in conjunction with the earlier results on contacts,
which are assumed to be determined only by demand, I hence find indirect evidence against
demand inducement among statutorily insured but for demand inducement among the
privately insured. This is because (1) among statutorily insured patients the elasticity of the
contact and the elasticity of the number of doctor visits with respect to physician density are
of the same size, (2) the frequency elasticity is (statistically) larger than the contact elasticity
among privately insured (at p<0.10). This key results is illustrated in Figure 3, which shows
the average predicted probability of physician contacts and the average predicted number of
physician visits conditional on visiting, separately for privately and statutorily insured
respondents.
--- about here Figure 3 --Let us also look at the effects of the covariates. Again, the estimates are fairly similar
across samples and specifications. Health itself has the expected strong impact on the
frequency of doctor visits. Conditional on covariates, the estimated number of visits of
respondents in the full sample who are in very poor health is about 5.8 times as large as the
number of visits of those in fair health.17 Respondents with hospital stays in the preceding
year go to the doctor 1.6 times as often as those without hospital stays.
Age plays an ambiguous role. In the full sample and among SHI patients, the effect is
U-shaped but hardly significant, among PHI patients is highly significant and hump-shaped
with a maximum at about age 50. Conditional on a visiting a doctor at all, education and
income have no significant effect on the frequency of physician visits. Gerdtham (1997)
reports similar results for Sweden and interprets this finding as evidence that patients' income
does not affect the decisions of physicians. Marital status (in the case of men) has no effect on
the frequency of visits. Thus married men contact a doctor more often than unmarried men
but conditional on contact they do not visit a doctor significantly more often. Conditional on
health, women visit doctors 1.2 times as often as men. Finally, being employed, full-time or
part-time, reduces the frequency of doctor visits by about 10 and 7 percent respectively.
17
This ratio is computed as exp[beta(very poor health)-beta(very good health)].
19
6. Summary and Conclusion
In this paper I have analyzed the relationship between health insurance status, regional
physician density (number of physicians per 100,000 inhabitants) and the frequency of
individual doctor visits in Germany in a negative binomial hurdle model. The hurdle model
statistically distinguishes between the decision to contact a physician (which is purely demand
driven) and the frequency of contact decision (which combines demand and supply aspects).
The paper added to earlier evidence from Germany in three respects: first, the analysis
explicitly distinguishes between privately and statutorily insured patients. This distinction has
proved crucial to arrive at the main finding of the paper. Conditional on health, privately
insured patients are less likely to contact a physician but more frequently visit a doctor
following a first contact. This finding is consistent with the idea that – if at all – physicians in
Germany induce privately insured patients to demand services beyond what is strictly
necessary. Physicians have an incentive to do this because patients with a private health
insurance are more attractive as they can be charged higher fees for the same services.
The second innovation in this paper in comparison to earlier studies using SOEP data
is that it uses an instrumental variable approach to account for the potential simultaneity of
physician density. I have chosen average district gross income, the percentage of inhabitants
aged 65 and over living in the district, and whether the district has a medical school as
instruments. The analysis shows that these instruments perform well in explaining physician
density and that they are conditionally unrelated to the main outcome variables, the
probability and frequency of individual doctor visits. However, it was also shown that an
instrumental variable approach is not necessary because the parameters of the instrumented
variable "physician density" do not differ significantly between the ordinary hurdle model and
the IV model.
Finally, the analyses combined more detailed regional data on physician density than
earlier studies with individual survey data on the frequency of doctor visits. Data on doctor
visits of some 20,000 individuals aged 17 to 99 were drawn from the German Socio-economic
panel 2002. Regional physician density was measured on the level of districts (Kreise), of
which Germany currently has 439 (the SOEP data used in this study contains information on
individuals from 434 of these districts). Similar studies with SOEP data have used regional
information on the state (Bundesland) level, which – due to measurement error – was
probably too coarse and resulted in downward biased estimates of the effect of physician
density.
20
Physician density has a significant positive effect on the doctor contact probability of
patients insured in the statutory health care system, whereas it has no effect on privately
insured patients' contact probability. This finding can be interpreted as evidence for the idea
that an increase in the number of doctors per inhabitant reduces the opportunity costs of
doctor visits for statutorily insured but not for privately insured. However, the effect of
physician density on the frequency of doctor visits is 1.6 times as large among privately than
among statutorily insured. In fact, I find an elasticity of 27 percent that is not only statistically
different from zero but also different from the contact probability elasticity.
Reverse causation and smaller opportunity costs can thus be excluded as explanations
for the rising number of doctor visits of privately insured patients as physician density
increases. Therefore, the findings presented in this paper give plausible albeit indirect
evidence for the hypothesis that in Germany, physicians tend to induce demand for medical
services among privately insured patients.
21
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23
Table 1: Sample description
Variable
Mean
StdDev
Min
Max
Individual level SHI patients (N=19,172)
# of doctor visits
Visited doctor
Conditional # of doctor visits*
Self-rated health: very good
Self-rated health: good
Self-rated health: fair
Self-rated health: poor
Self-rated health: very poor
Hospital stay in 2001
Age
Female
Married
Years of education
Log equivalent household income
Working full-time
Working part-time
Not working
2.57
0.69
3.75
0.09
0.40
0.34
0.14
0.04
0.12
47.42
0.53
0.64
11.70
9.79
0.41
0.23
0.36
4.24
0.46
4.67
0.28
0.49
0.47
0.34
0.19
0
0
1
0
0
0
0
0
0
17
0
0
7
7.53
0
0
0
90
1
90
1
1
1
1
1
1
99
1
1
18
13.14
1
1
1
Individual level PHI patients (N=3,245)
# of doctor visits
Visited doctor
Conditional # of doctor visits*
Deductible
Self-rated health: very good
Self-rated health: good
Self-rated health: fair
Self-rated health: poor
Self-rated health: very poor
Hospital stay in 2001
Age
Female
Married
Years of education
Log equivalent household income
Working full-time
Working part-time
Not working
2.31
0.63
3.67
0.40
0.13
0.47
0.29
0.09
0.01
0.10
48.29
0.39
0.72
14.48
10.32
0.61
0.18
0.21
0
0
1
0
0
0
0
0
0
0
17
0
0
7
7.68
0
0
0
50
1
50
1
1
1
1
1
1
1
93
1
1
18
13.37
1
1
1
70
11.3
12.4
0
1
383
80.6
23.0
1
782
District level (N=434)
Physicians / 100,000 inhabitants
150.4
Per capita income in €10,000
23.3
Percentage inhabitants aged 65+
17.8
Medical school
0.1
Number of individual observations
51.7
* conditional on visiting; N=13,173 (SHI), N=2,044 (PHI)
16.91
2.42
0.52
3.99
0.48
4.50
13.62
3.03
0.55
51.3
9.9
1.9
55.8
24
Table 2: First stage regression, OLS; dependent variable: log (physician density)
Variable
Full sample
SHI
Instruments (regional level variables)
Medical school
0.2527**
0.2532**
(0.0531)
(0.0529)
Percentage of inhabitants age 65+
0.0207**
0.0208**
(0.0075)
(0.0073)
Log income per capita
0.4575**
0.4573**
(0.0470)
(0.0461)
Individual level variables
PHI
Deductible
Very good health
Good health
Poor health
Very poor health
Hospital stay in 2001
Age
(Age/10)^2
Female
Married
Married*Female
Years of Education
Log equivalent hh income
Full Time Employed
Part Time Employed
Constant
N
Clusters
F statistic instruments
ΔR2 from including instruments
Note: * p<0.05; ** p<0.01
PHI
0.2479**
(0.0555)
0.0202*
(0.0095)
0.4612**
(0.0555)
0.0075
(0.0071)
-0.0025
(0.0068)
0.0030
(0.0083)
0.0007
(0.0044)
0.0017
(0.0036)
0.0027
(0.0076)
0.0064
(0.0041)
0.0007
(0.0006)
-0.0004
(0.0006)
0.0020
(0.0033)
-0.0220**
(0.0061)
0.0041
(0.0036)
0.0061**
(0.0011)
-0.0152**
(0.0058)
0.0048
(0.0037)
0.0014
(0.0037)
3.2074**
(0.2383)
0.0009
(0.0078)
-0.0018
(0.0045)
0.0019
(0.0039)
-0.0003
(0.0080)
0.0078
(0.0040)
0.0008
(0.0007)
-0.0003
(0.0007)
0.0032
(0.0036)
-0.0235**
(0.0068)
0.0035
(0.0043)
0.0072**
(0.0012)
-0.0165**
(0.0059)
0.0056
(0.0039)
0.0008
(0.0041)
3.2060**
(0.2339)
-0.0020
(0.0071)
0.0125
(0.0156)
0.0143
(0.0077)
-0.0021
(0.0135)
0.0367
(0.0278)
-0.0019
(0.0130)
0.0001
(0.0016)
0.0001
(0.0016)
-0.0129
(0.0141)
-0.0151
(0.0087)
0.0209
(0.0170)
0.0025
(0.0013)
-0.0106
(0.0109)
0.0054
(0.0100)
0.0098
(0.0098)
3.2261**
(0.2856)
22,417
434
70.37
0.62
19,172
433
73.31
0.62
3,245
394
55.40
0.62
25
Table 3. Logit regressions explaining whether a doctor was visited at all in last three months
Full sample
SHI sample
PHI sample
Logit
IV-Logita) Logit
IV-Logita) Logit
IV-Logita)
(1)
(2)
(3)
(4)
(5)
(6)
Log (Physician Density)
0.1488** 0.1297
0.1769** 0.1661*
-0.0045
-0.0357
(0.0537) (0.0685) (0.0595) (0.0749) (0.1258) (0.1620)
PHI
-0.1824** -0.1812**
(0.0568) (0.0558)
Deductible
-0.0704
-0.0706
-0.0618
-0.0615
(0.0797) (0.0814)
(0.0818) (0.0877)
Very good health
Good health
Fair health (reference category)
Poor health
Very poor health
Hospital stay in 2001
Age
(Age/10)^2
Female
Married
Married*Female
Years of Education
Log equivalent hh income
Full Time Employed
Part Time Employed
Constant
-1.2303**
(0.0556)
-0.6696**
(0.0364)
0.0000
-1.2292**
(0.0568)
-0.6693**
(0.0372)
0.0000
-1.2650**
(0.0618)
-0.6755**
(0.0397)
0.0000
-1.2642**
(0.0595)
-0.6753**
(0.0391)
0.0000
-1.0799**
(0.1281)
-0.6266**
(0.0924)
0.0000
-1.0781**
(0.1282)
-0.6258**
(0.0986)
0.0000
0.9555**
(0.0699)
1.5025**
(0.1742)
0.9364**
(0.0640)
0.9554**
(0.0756)
1.5016**
(0.1727)
0.9364**
(0.0612)
0.9560**
(0.0744)
1.5102**
(0.1818)
0.9225**
(0.0692)
0.9558**
(0.0751)
1.5088**
(0.1730)
0.9226**
(0.0639)
0.9661**
(0.2052)
1.3561*
(0.6139)
1.0479**
(0.1699)
0.9669**
(0.2208)
1.3584*
(0.6338)
1.0479**
(0.1736)
-0.0589**
(0.0069)
0.0769**
(0.0074)
0.6515**
(0.0523)
0.1661**
(0.0492)
-0.1315*
(0.0671)
0.0493**
(0.0066)
0.1829**
(0.0332)
-0.1305**
(0.0486)
-0.0514
(0.0491)
-1.5429**
(0.4146)
-0.0588**
(0.0067)
0.0768**
(0.0075)
0.6520**
(0.0533)
0.1649**
(0.0497)
-0.1321*
(0.0668)
0.0495**
(0.0070)
0.1832**
(0.0354)
-0.1308**
(0.0499)
-0.0514
(0.0506)
-1.4550**
(0.4885)
-0.0630**
(0.0074)
0.0829**
(0.0079)
0.6606**
(0.0561)
0.1540**
(0.0546)
-0.1265
(0.0727)
0.0575**
(0.0076)
0.1866**
(0.0368)
-0.1187*
(0.0523)
-0.0697
(0.0524)
-1.7592**
(0.4579)
-0.0629**
(0.0070)
0.0829**
(0.0077)
0.6612**
(0.0534)
0.1531**
(0.0495)
-0.1271
(0.0686)
0.0576**
(0.0079)
0.1867**
(0.0390)
-0.1188*
(0.0536)
-0.0696
(0.0545)
-1.7087**
(0.5282)
-0.0428*
(0.0211)
0.0495*
(0.0219)
0.5684**
(0.1501)
0.2285*
(0.1140)
-0.0907
(0.1832)
0.0291*
(0.0139)
0.1676*
(0.0779)
-0.1283
(0.1371)
0.1671
(0.1435)
-0.7254
(1.0202)
-0.0428
(0.0224)
0.0495*
(0.0238)
0.5687**
(0.1557)
0.2265
(0.1171)
-0.0901
(0.1878)
0.0294*
(0.0140)
0.1686*
(0.0820)
-0.1286
(0.1417)
0.1671
(0.1406)
-0.5830
(1.2509)
19,172
3053.42
0.1282
3,245
380.94
0.0891
.88
3,245
380.99
0.0891
N
22,417
22,417
19,172
Model Chi-Squared
3448.43
3444.48
3057.30
Pseudo-R2
0.1225
0.1224
0.1283
P-value of Hausman endogenity test
.83
.91
Note: a) Standard errors are bootstrapped (200 reps), * p<0.05, ** p<0.01
26
Table 4: Zero-truncated negative binomial regressions explaining the number of doctor visits in last three
months
Full sample
SHI sample
PHI sample
ZeroIV-Zero
ZeroIV-Zero
ZeroIV-Zero
Truncated Truncated Truncated Truncated Truncated Truncated
Negbin
Negbina) Negbin
Negbina) Negbin
Negbina)
(1)
(2)
(3)
(4)
(5)
(6)
Log (Physician Density)
0.1719** 0.2112** 0.1647** 0.2047** 0.2702** 0.3049*
(0.0344) (0.0532) (0.0367) (0.0572) (0.0993) (0.1449)
PHI
0.1816** 0.1787**
(0.0384) (0.0437)
Deductible
-0.0800
-0.0798
-0.0959
-0.0956
(0.0564) (0.0746)
(0.0639) (0.0781)
Very good health
Good health
Fair health (reference category)
Poor health
Very poor health
Hospital stay in 2001
Age
(Age/10)^2
Female
Married
Married*Female
Years of Education
Log equivalent hh income
Full Time Employed
Part Time Employed
Constant
Ln(alpha)
-0.7109**
(0.0495)
-0.5237**
(0.0252)
0.0000
-0.7110**
(0.0662)
-0.5232**
(0.0310)
0.0000
-0.6633**
(0.0546)
-0.5225**
(0.0271)
0.0000
-0.6636**
(0.0821)
-0.5216**
(0.0340)
0.0000
-0.8792**
(0.1199)
-0.5289**
(0.0694)
0.0000
-0.8777**
(0.1295)
-0.5311**
(0.0844)
0.0000
0.6070**
(0.0277)
1.0452**
(0.0449)
0.5093**
(0.0266)
0.6076**
(0.0305)
1.0395**
(0.0484)
0.5098**
(0.0301)
0.5874**
(0.0289)
1.0486**
(0.0456)
0.5045**
(0.0279)
0.5883**
(0.0327)
1.0432**
(0.0579)
0.5047**
(0.0334)
0.7961**
(0.0934)
0.9573**
(0.2021)
0.5404**
(0.0835)
0.7935**
(0.1031)
0.9518**
(0.2324)
0.5435**
(0.0946)
-0.0053
(0.0039)
0.0033
(0.0038)
0.1986**
(0.0362)
0.0473
(0.0358)
-0.0996*
(0.0448)
0.0025
(0.0043)
0.0022
(0.0215)
-0.1055**
(0.0306)
-0.0725*
(0.0307)
-0.0021
(0.2646)
0.0550
(0.0336)
-0.0053
(0.0048)
0.0034
(0.0047)
0.1945**
(0.0445)
0.0479
(0.0421)
-0.0963
(0.0519)
0.0022
(0.0051)
0.0016
(0.0256)
-0.1049**
(0.0379)
-0.0725
(0.0380)
-0.1872
(0.3706)
0.0537
(0.0497)
-0.0098*
(0.0040)
0.0075
(0.0039)
0.1966**
(0.0381)
0.0618
(0.0386)
-0.1087*
(0.0476)
0.0023
(0.0048)
0.0169
(0.0227)
-0.1056**
(0.0323)
-0.0784*
(0.0322)
0.0117
(0.2813)
0.0098
(0.0355)
-0.0098
(0.0052)
0.0075
(0.0051)
0.1919**
(0.0516)
0.0622
(0.0477)
-0.1048
(0.0612)
0.0019
(0.0062)
0.0163
(0.0266)
-0.1048*
(0.0419)
-0.0784*
(0.0395)
-0.1765
(0.3825)
0.0083
(0.0552)
0.0499**
(0.0139)
-0.0490**
(0.0137)
0.2630*
(0.1185)
-0.0292
(0.0969)
-0.1319
(0.1388)
0.0003
(0.0106)
-0.1076
(0.0637)
-0.1858
(0.0957)
-0.0742
(0.1006)
-0.5345
(0.8067)
0.3206**
(0.1042)
0.0492**
(0.0159)
-0.0482**
(0.0155)
0.2642*
(0.1298)
-0.0280
(0.1183)
-0.1337
(0.1542)
0.0004
(0.0131)
-0.1063
(0.0733)
-0.1851
(0.1135)
-0.0754
(0.1106)
-0.7117
(0.9403)
0.3217**
(0.1215)
13,175
2810.69
0.0495
2,044
413.75
0.0488
.84
2,044
412.30
0.0477
N
15,219
15,219
13,175
Model Chi-Squared
3190.92
3190.40
2810.94
Pseudo-R2
0.0488
0.0488
0.0495
P-value of Hausman endogenity test
.54
.56
Note: a) Standard errors are bootstrapped (200 reps), * p<0.05, ** p<0.01
27
Population
In labor force
Civil
servants
SelfEmployed
Employees
Above
income
threshold
Unemployed
Out of labor
force
Retirees
Same as
main earner
in household
Same as
before
retirement
Below
income
threshold
Right to choose between SHI, PHI,
and no insurance
Compulsory SHI
0
10
Percent
20
30
40
Figure 1: Stylised description of the German health insurance system
0
1
2
3
4
5
6
7-8 9-10 11-15 16-20 21-30 31-90
Number of doctor visits
SHI patients
PHI patients
Figure 2: Individual number of doctor visits in the last three months (SOEP 2002), by insurance status
.62
2.5
.64
Probability
.66
.68
3
3.5
Number of visits
.7
4
.72
28
70
100
150
250
Physician density (log scale)
SHI probability
SHI # visits
384
PHI probability
PHI # visits
Figure 3: Average predicted probability and average conditional number of doctor visits in the last three months
(SOEP 2002), by physician density and insurance status. Predictions are based on Table 4, columns 3 and 5 and
Table 5, columns 3 and 5
Discussion Paper Series
Mannheim Research Institute for the Economics of Aging Universität Mannheim
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